Using vectors, find displacement.

Question

The hour hand of a world famous clock is 2.74M long while the minute hand is 4.2M long.

1. Determine the displacement from the tip of the hour hand at -12.30 and 13.17
2. Calculate distance travelled and displacement of the tip of each hand between 23:15 and 02:15 the next day

Answer 1

For 1 hour , the hour hands travels angle = 2pi/12 radians

 

Time between 12:30 to 13:17 = 47 minutes = 47/60 hr = 0.783 hrs

 

So angle covered in 47 minutes = 0.783 x 2pi/12 radians = 0.41 radians 

 

Displacement of the tip of the hour hand = angle x radius = 0.41 x 2.74 m  = 1.124 m

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Similarly there are 2 hours between 23:15 to 02:15. 

 

Angle covered by hour hand = 2 x 2pi/12 radians

Distance covered by hour hand = radius x angle  =  2.74 x 2 x 2pi/12 m = 2.87 m

 

Angle covered by minute hand = 2 x 2pi = 4pi radians

Distance covered by minute hand = radius x angle = 4.2 x 4pi m  = 52.78 m